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LING 364: Introduction to Formal Semantics

LING 364: Introduction to Formal Semantics. Lecture 9 February 9th. Administrivia. Reminder Homework 2 due next Tuesday need help getting started ?. Administrivia. today (3:30pm – 4:40pm) lecture here in Comm 214 (4:45pm – 5:45pm) ( EXTRA) lab practice in Social Sciences Lab 224

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LING 364: Introduction to Formal Semantics

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  1. LING 364: Introduction to Formal Semantics Lecture 9 February 9th

  2. Administrivia • Reminder • Homework 2 due next Tuesday • need help getting started?

  3. Administrivia • today • (3:30pm – 4:40pm) • lecture here in Comm 214 • (4:45pm – 5:45pm) (EXTRA) • lab practice in Social Sciences Lab 224 • we’ll begin doing the homework exercises in the lab

  4. Today’s Topics • Grammar Rule Recursion • Prolog behavior • Handout (from Tuesday) • Chapter 3: More about Predicates • Short Quiz #3 on Thursday

  5. Grammar Rule Recursion • Recursion: • A phrase may contain embedded inside another instance of the same phrase • Example: • sentence with a relative clause • [Sbar [S I saw [NP the man [Sbar who [S attacked me]]]]] • [Sbar [S I saw [NP the man [Sbar who [S attacked [NP the dog [Sbar who [S attacked me ]]]]]]]]

  6. Grammar Rule Recursion • Example: • assuming NP (not DP analysis) for simplicity... • [NP [NP John] ’s mother] • [NP [NP [NP John]’s mother]’s cat] • DCG rules: • np --> np, [‘‘‘s‘], n. • n --> [mother]. • n --> [cat]. • np --> [john]. ‘‘‘s‘ = ‘s

  7. Grammar Rule Recursion • Prolog Computation Rule: • select “first” matching grammar rule each time we call a non-terminal • “first” = first line that matches • DCG rules: • np --> np, [‘‘‘s‘], n. • n --> [mother]. • n --> [cat]. • np --> [john]. • Leads to infinite loop here...

  8. Grammar Rule Recursion • General Rule for writing recursive rules: • put recursive case last • i.e. place non-recursive rules for a non-terminal ahead of the recursive ones • DCG rules: • np --> [john]. • np --> np, [‘‘‘s‘], n. • n --> [mother]. • n --> [cat]. • no looping here...

  9. Grammar Rule Recursion • You’ll need it for homework 2... • Examples: • [Sbar [NP Who] [S [VP [V is] [NP[NP [DET a][N student]]]]][CONJ and][NP [DET a][N baseball fan]]]]]] • [Sbar [NP Who] [S [VP [V is] [NP[NP [DET a][N student]]]]][CONJ and][NP [NEG not][NP[DET a][N baseball fan]]]]]]] • Consider a possible NP rule for conjoining two NPs: • np --> np, conj, np. • conj --> [and].

  10. More about Predicates • 3.1 Other Types of Predicates: Adjectives, Predicate Nominals • (1) Shelby is small • (2) Shelby is a dog • Semantics of is and a. • Possibilities: • Meaningless • Non-interfering meaning - trivial meaning

  11. More about Predicates • 3.1 Other Types of Predicates: Adjectives, Predicate Nominals • (1) Shelby is small • (2) Shelby is a dog • Semantics of (indefinite determiner) a. • (3) a dog bit me • (4) the/one/every dog bit me • quantifier?

  12. More about Predicates • Semantics of (indefinite determiner) a. • (3) a dog bit me • (4) the/one/every dog bit me • quantifier? • (3’) there exists a dog x such that bit(x,me) • (4’) every: for each dog x, bit(x,me)

  13. More about Predicates • Semantics of (indefinite determiner) a. • (3) a dog bit me • (3’) there exists a dog x such that bit(x,me) • (2) Shelby is a dog • semantics involving “there exist a dog x”

  14. More about Predicates • Semantics of (indefinite determiner) a. • (3) a dog bit me • (3’) there exists a dog x such that bit(x,me) • (2) Shelby is a dog • semantics involving “there exist a dog x” • No...

  15. More about Predicates • 3.2 Transitive Verbs • (5) Shelby saw Hannibal • 3.3 Relative Clauses • (7) Hannibal is [who Shelby saw] • semantics of [who Shelby saw]

  16. More about Predicates • 3.3 Relative Clauses • (7) Hannibal is [who Shelby saw] • semantics of [who Shelby saw] • Shelby saw who saw(shelby,who). • (with logic variable) saw(shelby,X).

  17. More about Predicates • 3.4 Topicalization • (9) Shelby, Mary saw • Semantics? • Paraphrase (9) as: • (10) Shelby is who1 Mary saw e1

  18. More about Predicates • 3.5 Sub-atomic Semantics • Event semantics • (11) Sylvia petted Shelby • introduce an event variable, call it e • Prolog-style, we can say: • event(e), agent(e,sylvia), patient(e,shelby). • Notions like: • agent, patient, instrument etc. are called thematic roles

  19. More about Predicates • lambda calculus: • easy to introduce now... • Example: • barks: λx.x barks barks(X). • Shelby barks • [λx.x barks](Shelby) • barks(X), X = shelby • Generalization: • [λx.[λy.y saw x]

  20. Quiz 3 • (3pts) • Give lambda calculus semantics for: • likes • likes Mary • John likes Mary

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